The Hopf's limiting cycle -- A method to measure the electron cooling force

[摘要] The longitudinal phase space structure of protons in the presence of an electron drag force is studied. Depending on the relative difference in average proton velocity and electron velocity, the fixed point near the center of the phase space can be stable or unstable. When it is unstable, a stable Hopf's limit cycle exists. By measuring the appearance and size of the Hopf's limit cycle, the electron cooling force can be deduced.

[发布日期] 2002-09-30 [发布机构] Fermi National Accelerator Laboratory

[关键词] Protons;71 Classical And Quantum Mechanics, General Physics;Electron Cooling;Limit Cycle;72 Physics Of Elementary Particles And Fields